Many empirical studies attempt to estimate the elasticity of labor demand. 6 Given our ear- lier discussion of the problems encountered in estimating the labor supply elasticity, it should not be too surprising that there is a huge range of variation in the estimates of the labor demand elasticity. Although most of the estimates indicate that the labor demand curve is downward sloping, the range of the estimates is very wide.
6 An encyclopedic survey of this literature is given by Daniel S. Hamermesh, Labor Demand, Princeton, NJ: Princeton University Press, 1993.
Dollars
Employment Long-Run
Demand Curve Short-Run
Demand Curve
FIGURE 3-13 The Short- and Long-Run Demand Curves for Labor
In the long run, the firm can take full advantage of the economic opportunities introduced by a change in the wage. As a result, the long-run demand curve is more elastic than the short-run demand curve.
104
Despite the dispersion in the estimates of the short-run labor demand elasticity, there is some consensus that the elasticity lies between 0.4 and 0.5. In other words, a 10 percent increase in the wage reduces employment by perhaps 4 to 5 percentage points in the short run. The evidence also suggests that the estimates of the long-run labor demand elasticity
The Fair Labor Standards Act of 1938 requires that cov- ered workers be paid 1.5 times the wage for any hours worked in excess of 40 hours per week. Unlike most states, California imposes additional regulations on over- time pay. Workers in California must be paid 1.5 times the wage for any hours worked in excess of 8 hours per day—even if they work fewer than 40 hours during the week. Before 1974, California’s legislation applied only to female workers. After 1980, the legislation covers both men and women.
The theory of labor demand makes a clear prediction about how this legislation should affect the probability that California’s workers work more than eight hours per day. In particular, the probability that men work more than eight hours per day in California should have declined between the 1970s and the 1980s—as the over- time-per-day regulation was extended to cover men and employers switched to cheaper methods of production.
Table 3-2 shows that 17.1 percent of California’s working men worked more than eight hours per day in 1973. By 1985, only 16.9 percent of working men worked more than eight hours per day.
Before we can attribute this slight reduction in the length of the workday to the increasing coverage of the over- time legislation, we need to know what would have hap- pened to the length of the workday for California’s men in the absence of the legislation. In other words, we need a control group. One possible control group is the working men in other states—men whose workday was unaffected by the change in California’s policies. It turns out that the fraction of men in other states working more than eight hours per day rose during the same period, from 20.1 to 22.8 percent. The “difference-in-differences”
estimate of the impact of California’s overtime legisla- tion was a substantial reduction of 2.9 percentage points on the probability of working more than eight hours per day. Alternatively, the control group could be California’s working women—who had always been covered by the legislation. The probability that their workday lasted more than eight hours also rose during the period, from 4.0 to 7.2 percent. Again, the difference-in-differences approach implies that California’s overtime legislation reduced the probability that working men worked more than eight hours per day by 3.4 percentage points.
Theory at Work
CALIFORNIA’S OVERTIME REGULATIONS AND LABOR DEMAND
TABLE 3-2 Employment Effects of Overtime Regulation in California
Source: Daniel S. Hamermesh and Stephen J. Trejo, “The Demand for Hours of Labor: Direct Estimates from California,” Review of Economics and Statistics 82 (February 2000): 38–47.
Treatment Group Control Group
Men in California (%) Men in Other States (%) Women in California (%) Workers working more
than 8 hours per day in
1973 17.1 20.1 4.0
1985 16.9 22.8 7.2
Difference 0.2 2.7 3.2
Difference-in-differences — ⴚ2.9 ⴚ3.4
cluster around 1, so the long-run labor demand curve is indeed more elastic than the short-run curve. In the long run, a 10 percent change in the wage leads to a 10 percent change in employment. About one-third of the long-run elasticity can be attributed to the substitution effect and about two-thirds to the scale effect.
3-5 The Elasticity of Substitution
The size of the firm’s substitution effect depends on the curvature of the isoquant. Two extreme situations are illustrated in Figure 3-14 . In Figure 3-14 a, the isoquant is a straight line, with a slope equal to –0.5. In other words, output remains constant whenever the firm lays off two workers and replaces them with one machine. This “rate of exchange” between labor and capital is the same regardless of how many workers or how much capital the firm already has. The marginal rate of technical substitution is constant when the isoquant is a line. Whenever any two inputs in production can be substituted at a constant rate, the two inputs are called perfect substitutes. 7
The other extreme is illustrated in Figure 3-14 b . The right-angled isoquant implies that using 20 workers and 5 machines yields q 0 units of output. If we hold capital constant at five units, adding more workers has no impact on output. Similarly, if we hold labor FIGURE 3-14 Isoquants When Inputs Are Either Perfect Substitutes or Perfect Complements
Capital and labor are perfect substitutes if the isoquant is linear (so that two workers can always be substituted for one machine). The two inputs are perfect complements if the isoquant is right-angled. The firm then gets the same output when it hires 5 machines and 20 workers as when it hires 5 machines and 25 workers.
Capital
100
200 Employment q0 Isoquant
(a) Perfect Substitutes
Capital
5
20 Employment
q0 Isoquant
(b) Perfect Complements
7 Note that our definition of perfect substitution does not imply that the two inputs have to be exchanged on a one-to-one basis; that is, one machine hired for each worker laid off. Our definition implies only that the rate at which capital can be replaced for labor is constant.
constant at 20 workers, adding more machines has no impact on output. A firm that does not wish to throw away money has only one recipe for producing q 0 units of output: use 20 workers and 5 machines! When the isoquant between any two inputs is right-angled, the two inputs are called perfect complements .
The substitution effect is very large when labor and capital are perfect substitutes.
When the isoquant is linear, the firm minimizes the costs of producing q 0 units of output by hiring either 100 machines or 200 workers, depending on which of these two alterna- tives is cheaper. If the prices of the inputs change sufficiently, the firm will jump from one extreme to the other.
In contrast, there is no substitution effect when the two inputs are perfect complements.
Because there is only one recipe for producing q 0 units of output, a change in the wage does not alter the input mix at all. The firm must always use 20 workers and 5 machines to produce q 0 units of output, regardless of the price of labor and capital.
In between these two extremes, there are a great number of substitution possibilities, depending on the curvature of the isoquant. The more curved the isoquant, the smaller the size of the substitution effect. To measure the curvature of the isoquant, we typically use a number called the elasticity of substitution. The elasticity of substitution between capital and labor (holding output constant) is defined by
Elasticity of substitution =
Percent change in (K兾E)
Percent change in (w兾r) (3-17) The elasticity of substitution gives the percentage change in the capital/labor ratio result- ing from a 1 percent change in the relative price of labor. As the relative price of labor increases, the substitution effect tells us that the capital/labor ratio increases (that is, the firm gets rid of labor and replaces it with capital). The elasticity of substitution, therefore, is defined so that it is a positive number. It turns out that the elasticity of substitution is zero if the isoquant is right-angled, as in Figure 3-14 b, and is infinite if the isoquant is linear, as in Figure 3-14 a . The size of the substitution effect, therefore, directly depends on the magnitude of the elasticity of substitution.
3-6 Policy Application: Affirmative Action and Production Costs
There has been a great deal of debate about the economic impact of affirmative action programs in the labor market. These programs typically “encourage” firms to alter the race, ethnicity, or gender of their workforce by hiring relatively more of those workers who have been underrepresented in the firm’s hiring in the past. A particular affirmative action plan, for instance, might require that the firm hire one black worker for every two workers hired.
Our theory of how firms choose the optimal mix of inputs in the production process helps us understand the nature of the debate over the employment impact of these pro- grams. To simplify the discussion, suppose there are two inputs in the production process:
black workers and white workers. In this example, therefore, we will ignore the role that capital plays in the firm’s production. This simplification allows us to represent the firm’s hiring choices in terms of the two-dimensional isocosts and isoquants that we derived in
the earlier sections. Suppose further that black and white workers are not perfect substi- tutes in production, so that the isoquants between these two groups have the usual convex shape, as illustrated in Figure 3-15 a . The two groups of workers might have different pro- ductivities because they might differ in the amount and quality of educational attainment, or because they might have been employed in different occupations and hence are entering this firm with different types of job training.
A competitive firm can hire as many black workers as it wants at the going wage of w B and can hire as many white workers as it wants at the going wage of w W . A firm is
“color-blind” if the race of the workers does not enter the hiring decision at all. A profit- maximizing color-blind firm would then want to produce q * units of output in the most effi- cient way possible, where the isoquant is tangent to the isocost. This hiring mix is illustrated by point Q in Figure 3-15 a .
FIGURE 3-15 Affirmative Action and the Costs of Production
(a) The discriminatory firm chooses the input mix at point P, ignoring the cost-minimizing rule that the isoquant be tangent to the isocost. An affirmative action program can force the firm to move to point Q, resulting in more efficient production and lower costs. (b) A color-blind firm is at point P, hiring relatively more whites because of the shape of the isoquants. An affirmative action program increases this firm’s costs.
Black Labor
100
White Labor q*
(a) Affirmative Action Reduces Costs of Discriminatory Firm Q
P
Black Labor
White Labor q*
(b) Affirmative Action Increases Costs of Color-Blind Firm
Q
P
Suppose, however, that the firm discriminates against black workers. In other words, the firm’s management gets disutility from hiring blacks and would rather see whites filling most jobs in the firm. The firm’s prejudice alters its hiring decision. A discriminatory firm will not want to be at point Q, but instead will choose an input mix that has more white workers and fewer black workers to produce the same q * units of output, such as point P in the figure.
Note that employment discrimination moves the firm away from the input mix where the isoquant is tangent to the isocost. The prejudiced firm has simply decided that it is going to ignore the cost-minimizing rule because that rule generates the “wrong” color mix for the firm’s workforce. As a result, the input mix chosen by the firm (or point P ) is no longer a point where the isoquant is tangent to the isocost. After all, the slope of the isocost is given by the ratio of wage rates (or – w W / w B ), and a competitive firm cannot influ- ence wages. Therefore, point P does not lie on the lowest isocost that would allow the firm to produce q * units of output, and the prejudiced firm uses an input combination that costs more than the input combination it would have chosen had it been a color-blind firm. Our theoretical framework, therefore, leads to a very simple— and surprising —conclusion:
Discrimination is not profitable. 8
Suppose that the government forces the firm to adopt an affirmative action program that mandates the firm hire relatively more blacks. This policy moves the firm’s employ- ment decision closer to the input mix that a color-blind firm would have chosen. In fact, if the government fine-tunes the employment quota “just right,” it could force the discrimina- tory firm to hire the same input mix as a color-blind firm (or point Q ).
This type of affirmative action policy has two interesting consequences. First, the firm’s workforce has relatively more blacks. And, second, because it costs less to produce a par- ticular level of output, the firm is more profitable. 9 In short, this type of affirmative action policy leads to a more efficient allocation of resources. The reason is that discriminatory firms are ignoring the underlying economic fundamentals. In particular, they disregard the information provided by the cost of hiring black and white workers when they make their hiring decisions, and instead go with their “feelings.” Affirmative action policies would then force discriminatory firms to pay more attention to prices.
Before we conclude that the widespread adoption of affirmative action programs would be a boon to a competitive economy, it is important to recognize that the example illus- trated in Figure 3-15 a adopted a particular prism through which to view the world. In par- ticular, the analysis assumed that the competitive firm is prejudiced, so that the firm’s hiring decisions are affected by discrimination.
Needless to say, there is an alternative point of view, one that leads to very different implications. Suppose, in particular, that firms in the labor market do not discriminate at all against black workers. And suppose further that the shape of the firm’s isoquants is such
8 This conclusion was first derived in Gary S. Becker, The Economics of Discrimination, Chicago: Univer- sity of Chicago Press, 1957. Chapter 9 presents a much more detailed discussion of discrimination in the labor market. In this section, we use the context of discrimination to show how our approach to modeling the firm’s employment decision can inform us about the nature of the debate over many policy-relevant issues.
9 Because the affirmative action program increases the demand for black workers and reduces the demand for white workers, the program also will tend to equalize the wages of black and white workers in the labor market.
that the firm hires relatively fewer black workers, even if blacks and whites are equally costly. This situation is illustrated in Figure 13-15 b, where the slope of the isocost is minus one. The color-blind profit-maximizing firm then chooses the input mix at point P in the figure, where the isoquant is tangent to the isocost and the firm is producing output q * in the cheapest way possible. Because of productivity differences between the two groups, this color-blind firm hires a workforce that has many white workers and relatively few black workers.
Suppose the government again mandates that firms hire relatively more blacks. This pol- icy forces the firm to move from point P, the cost-minimizing solution, to point Q, a point where the isoquant is not tangent to the isocost. Therefore, this affirmative action program increases the firm’s costs of production.
It is clear, therefore, that the “initial conditions” assumed in the exercise determine the inferences that one draws about the labor market impact of affirmative action programs.
If one assumes that the typical competitive firm discriminates against black workers, an affirmative action program forces the firm to pay more attention to the economic funda- mentals and increases the firm’s profits. In contrast, if one assumes that the typical firm does not discriminate, an affirmative action program may substantially reduce the profit- ability of competitive firms and perhaps drive many of them out of business. 10
As this discussion shows, our perception about the “real world” can greatly influence the position that we take in the debate over the labor market impacts of affirmative action.
This fact reinforces the importance of couching the debate in the context of the empirical evidence about the existence and prevalence of labor market discrimination. As we will see in Chapter 9, labor economists have made a great deal of progress in trying to understand the factors that encourage firms to take race into account when they make hiring deci- sions and have derived widely used methodologies to measure the extent of labor market discrimination.
3-7 Marshall’s Rules of Derived Demand
The famous Marshall’s rules of derived demand describe the situations that are likely to generate elastic labor demand curves in a particular industry. 11 In particular:
• Labor demand is more elastic the greater the elasticity of substitution. This rule fol-
lows from the fact that the size of the substitution effect depends on the curvature of the isoquant. The greater the elasticity of substitution, the more the isoquant looks like a straight line, and the more “similar” labor and capital are in the production process.
This allows the firm to easily substitute labor for capital as the wage increases.
10 The evidence on whether affirmative action programs increase or reduce the firm’s costs is incon- clusive. See Jonathan Leonard, “Anti-Discrimination or Reverse Discrimination? The Impact of Chang- ing Demographics, Title VII, and Affirmative Action on Productivity,” Journal of Human Resources 19 (Spring 1984): 145–174; and Peter Griffin, “The Impact of Affirmative Action on Labor Demand:
A Test of Some Implications of the Le Chatelier Principle,” Review of Economics and Statistics 74 (May 1992): 251–260. A good survey of the literature is given by Harry Holzer and David Neumark,
“Assessing Affirmative Action,” Journal of Economic Literature 38 (September 2000): 483–568.
11 The mathematical appendix presents a partial derivation of these rules. For a more technical, but complete derivation, see Hamermesh, Labor Demand.
• Labor demand is more elastic the greater the elasticity of demand for the output. When the wage rises, the marginal cost of production increases. A wage increase, therefore, raises the industry’s price and reduces consumers’ demand for the product. Because less output is being sold, firms cut employment. The greater the reduction in consumer demand (that is, the more elastic the demand curve for the output), the larger the cut in employment and the more elastic the industry’s labor demand curve.
• Labor demand is more elastic the greater labor’s share in total costs. Suppose labor is a relatively “important” input in the production process, in the sense that labor’s share of total costs is large. This situation might occur, for example, when production is very labor intensive, as with a firm using highly trained craftspeople to produce expensive handmade ornaments. In this case, even a small increase in the wage rate would sub- stantially increase the marginal cost of production. This increase in marginal cost raises the output price and induces consumers to cut back on their purchases of the ornaments.
Firms, in turn, would cut back on employment substantially. In contrast, if labor is
“unimportant,” so that labor makes up only a small share of total costs, a wage increase has only a small impact on marginal cost, on the price of the output, and on consumer demand. There is little need for the firm’s employment to shrink. 12
• The demand for labor is more elastic the greater the supply elasticity of other factors
of production, such as capital. We have assumed that firms can hire as much capital as they want at the constant price r. Suppose there is a wage increase and firms want to substitute from labor to capital. If the supply curve of capital is inelastic, so that the price of capital increases substantially as more and more capital is hired, the economic incentives for moving along an isoquant are greatly reduced. In other words, it is not quite as profitable to get rid of labor and employ capital instead. The demand curve for labor, therefore, is more elastic the easier it is to increase the capital stock (that is, the more elastic the supply curve of capital).